Inspired by modelling phenomena in biology, I'm wondering whether there has been mathematical study on the following question:
Given some $\mathbf{X}(t) \in \mathbb{R}^n$, find $f = f(X_1, \dots, X_n)$, where $f$ is time invariant so that $$X'(t) = f(X_1, \dots, X_n)$$
To explain, has there been an exposition into the general problem of finding a time invariant differential equation which "best" describes the time evolution of a given system?